Sentence examples for and define on from inspiring English sources

Set, and define on as follows: (4.3).

Assume that is convex and u.s.c. with nonempty convex compact values, and define on by for.

Denote (Z:= Xtimes X) and define on Z, for (z:= x,y), w:= u,v in Z), the partial order relation zpreceq w quad mbox{if and only if}quad (xgeq u mbox{ and } yleq v).

Inventions should be named, and invented terms for parts or systems that are required to make the invention work should be identified and defined on the blueprint.

The paper describes a new model for the problem that is based on multicommodity flows with unknown destinations and defined on a discretization of the plane.

This study reiterates the need for bycatch issues to be clearly identified and defined on a fishery-specific basis, and prior to the implementation of mitigation measures.

The density implies the existence of the adjoint operators and, for and, defined on Hγ ℝ2).

The regions are based and defined on political (municipality) and geographical boundaries.

Consider two arbitrary convex functions and defined on satisfying conditions (3.1) and (3.2).

Now we introduce the following bilinear mappings and defined on as.

With the aid of Lemma 3.1, we introduce the integral functionals and defined on and, respectively, given by (3.11).